Rewrite as a simplified fraction. ${1.28\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1286.6666...\\ 100x &= 128.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1158}$ ${x = \dfrac{1158}{900}} $ ${x = \dfrac{193}{150}} \text{or} {1 \dfrac{43}{150}}$